A new method for assessment of regional drought risk: information diffusion and interval mapping adjustment based on k-means cluster points

CRITIC

Crtiteria Importance Through Intercriteria Correlation

ED

extreme drought

IPCC

Intergovernmental Panel on Climate Change

IDWI

inverse distance weight interpolation

IMA

interval mapping adjustment

MND

multidimensional normal diffusion

ND

no drought

MID

mild drought

MOD

moderate drought

SD

severe drought

WCA

weighted comprehensive assessment

In the Sixth IPCC (Intergovernmental Panel on Climate Change) Assessment Report, it is pointed out that global warming has caused the increase of atmospheric evaporation demand and drought events (IPCC 2021). Drought events tend to have a serious impact on production, life and ecology due to its long latency and duration. The losses caused by drought can be effectively reduced and the ability to cope with drought can be enhanced by drought risk management. In recent years, drought risk management has been transformed from single drought resistance to comprehensive drought resistance (Xu et al. 2013), in which region-oriented assessment of drought risk is the core content of drought risk management, as well as the main means of regional sustainable development management and combating global climate change (Jin et al. 2016). At present, there are three assessment theoretical modes of regional drought (Jin et al. 2016): the first is the curve assessment method based on the analysis of historical drought loss frequency, the second is the curve assessment method based on the physical genetic process of drought loss risk and the third is the assessment of drought risk based on the components of drought risk loss (hereinafter referred to as weighted comprehensive assessment method (WCA)). The WCA can build assessment indicator system of drought risk according to the difference of different regional differentiation, and the weight calculation results can reflect the influence of various factors contributing to drought risk. The WCA helps to analyse the overall regional drought risk, which has been widely used with its low data requirements, strong operability and flexibility (Ai et al. 2020; Wang et al. 2021a).

At present, there are many studies on the assessment of regional drought risk using conventional WCA. Chou et al. (2019) used the analytic hierarchy process (AHP) to calculate the risk values of hazard, vulnerability and exposure of vulnerable eco-regions in China during 1988–2017, and predicted the change of drought risk in the future. Zhao et al. (2020) made a quantitative analysis of drought risk in China from three aspects: hazard, vulnerability and exposure, and found out the main influencing factors. Huang et al. (2015) constructed an integrated drought index combining meteorological, hydrological and agricultural factors based on the variable fuzzy set theory and calculated the spatial distribution characteristics of the annual average and seasonal average integrated drought index in the Yellow River Basin. Through the analysis of the above studies, the drought risk of the assessment objects in the region can be compared by the conventional WCA, i.e., the relative quantification of drought risk (Jin et al. 2016). However, it is difficult to carry out classification of risk grade directly. The cluster analysis had been introduced into the assessment of drought risk to classify research objects in some studies. Shim et al. (2021) used k-means clustering (clustering based on Euclidean distance between sample data) to divide South Korean island areas into three clusters for the assessment of drought vulnerability and pointed out the main vulnerability factors affecting each cluster. Moura et al. (2021) identify homogenous zones over Paraiba State in relation to the state, duration and severity of droughts that have occurred during 1998–2017 using hierarchical clustering based on rainfall data. The risk grades of the research areas according to the drought risk values were only classified but the risk values of the assessment objects were not assigned in the above two studies, and the results could not reflect the distinction between the drought risk values of different assessment objects in the same grade. According to the above defects, some researchers refined risk value. Tang et al. (2009) classified the grade on the basis of comprehensive drought risk value of each city in Anhui Province calculated by the conventional mutation evaluation method and mapped the comprehensive drought risk values to 10 uniform interval range 0–1 by interval mapping adjustment (IMA). Thus, the differentiation degree of risk value of each city can be increased, and the grade and size of evaluation value can be shown more intuitively. Qu et al. (2015) constructed the evaluation index system from the perspectives of hazard causing factors, hazard bearing bodies and hazard-pregnant environment, and calculated the agricultural drought risk degree of all provinces in China based on the WCA and AHP. After determining the grade division of a single index by using the normal distribution, the fuzzy comprehensive evaluation method was used to classify and assign the grade of hazard, vulnerability and exposure. Sahana et al. (2021) divided drought index ranging from 0 to 1 into five grades based on calculating the drought hazard index and the drought vulnerability index by multivariate standardized drought index and determined the number of each category by k-means clustering. To sum up, it can be found that there is the defect for the conventional WCA in the division of risk grade. At the same time, the combination of machine learning and drought research is one of the mainstream methods. Machine learning is a reliable choice for both assessing current drought risk and predicting future drought trends (Shamshirband et al. 2020; Band et al. 2022).

This paper aimed to solve the defect that conventional WCA cannot grade drought risk and referred to the research idea that k-means clustering was used to classify the drought area in other literature works, and k-means clustering was introduced to grade drought risk. In order to improve the discrimination degree of risk value of the assessment objects, the drought risks of the assessment objects were quantified by using IDWI and MND, respectively, on the basis of the calculation for the risk value of cluster points. Finally, the risk grade was shown more accurately through IMA, which provided a new idea for the assessment of regional drought risk.

Regional drought system is a nonlinear dynamical system coupled by regional natural, economic and social factors, which is characterized by non-stationarity (Luo et al. 2019). In this study, assessment indicators are selected from three aspects which make up the nature disaster system, including hazard of disaster causing factors, vulnerability of disaster bearing environment and vulnerability of disaster affected bodies, to jointly construct a drought risk assessment indicator system in the Anhui Province. The data used from 2000 to 2020 are from the Anhui Statistical Yearbook (http://tjj.ah.gov.cn/ssah/qwfbjd/tjnj/index.html), 65 Years of Flood Control and Drought Relief in Anhui Province (Compiled by Anhui Flood Control and Drought Relief Headquarters Office), Flood and Drought Disasters in Anhui Province (Compiled by Department of Water Resources in Anhui Province), Drought Resistance Manual of Anhui Province (Compiled by Department of Water Resources in Anhui Province), etc. The above data are the annual scale data of the Anhui Province from 2000 to 2020, reflecting the overall level of Anhui Province in each year.

Based on previous research results (Tang 2008; Tang et al. 2009) and related studies (Fang et al. 2019; Kyatengerwa et al. 2020), and considering the accessibility of index data, eight indicators including precipitation anomaly percentage, temperature anomaly percentage, water resources per unit area, proportion of primary output value, proportion of effective irrigated area in cultivated land area, proportion of cultivated land, proportion of animal husbandry and forestry output value and proportion of agricultural population were selected as drought risk assessment indicators in this study, and they can respond to the driving mechanism of drought system.

The Criteria Importance Through Intercriteria Correlation (CRITIC) method was proposed by Diakoulaki in 1995, which measured the objective weight of indicators based on the contrast intensity and conflict between indicators and its weight was more reasonable and stable than independence weighting method, entropy weighting method, coefficient of variation method (Diakoulaki et al. 1995; Wang et al. 2022). The weight is calculated as follows:

K-means clustering is an unsupervised clustering algorithm, which has good applicability in drought assessment (Leščešen et al. 2019). k-means clustering algorithm is characterized by simple implementation, efficient and concise, and its clustering of drought risk grade is more objective than artificial classification. Data are usually divided into k clusters according to the Euclidean distance and the initial cluster results are optimized through iteration. The main steps are as follows (Yan et al. 2022):

• k samples were selected from the standardized samples in Section 2.2.1.1 as the initial cluster centers ⁠.

• Calculate the distance from each sample to cluster centers in the dataset and divide it into the cluster whose cluster center with the smallest distance to ⁠.

• According to the cluster result, recalculate the new cluster center ⁠:

  

  (8)

• Repeat Steps (2) and (3) until the termination iteration condition (usually the number of iterations, the minimum error) is reached. So far, the samples have been clustered into k classes and the clustering center of each class can be obtained.

The information redistribution of cluster point based on IDWI is to combine k-means clustering and IDWI to requantify the risk value of the assessment objects in the same risk grade. After k clusters and their cluster centers are obtained by k-means clustering, the risk value of each cluster center is calculated based on the weight obtained by CRITIC weighting method and the risk value of each cluster member is obtained by IDWI. The main steps are as follows (Imen et al. 2021):

• Calculate the square of the distance from cluster members to each cluster center D (Ohlert et al. 2022)

  

  (10)

  where is the cluster member and is the cluster center.
• Calculate the weight of cluster members to each cluster center

  

  (10)
• Calculate the risk value at each cluster member

  

  (12)

  where is the risk value of the cluster center.

The information redistribution of cluster point based on MND is similar to the information redistribution based on IDWI. The difference is that the information of cluster points is diffused to each cluster member through the MND after calculating the risk value of each cluster center, namely get drought risk value of each year in Anhui Province. The main processes of MND are as follows (Huang & Shi 2002):

• P is a sample set containing m sample points, and each sample point contains n components. The sample is denoted by ⁠, and its domain is denoted by and ⁠, which is denoted by ⁠. In the case of this study, P is the cluster center sample set, and U is the standardized data set of the assessment indicator.

• According to the principle of information diffusion, the information carried by the sample points in P is allocated to the points in according to by the MND, the formula is as follows (Yu et al. 2020; Zhang et al. 2022):

  

  (13)

Considering that the risk quantification method based on cluster points is closely related to the risk value of cluster centers, and the risk value of cluster centers is close to each other, which cause the little inter-annual variation between the risk value of the assessment objects after quantification, and the discrimination of drought risk value of different years between different risk grades will be low. Therefore, it is considered to map the quantified risk to the range of [0,1], which can not only affect the classification result of drought risk grade, but also make the discrimination degree of risk values in the same grade or different grades more obvious. The mapping process is as follows:

• According to the risk value of cluster centers, the k-means cluster results were set into five grades: No drought (ND) – mild drought (MID) – moderate drought (MOD) – severe drought (SD) – extreme drought (ED). were, respectively, set as the minimum value of the four grades range from MID to ED after the quantification to risk of the assessment objects, and they were defined as the classification thresholds of the grades range from ND to ED, namely and ⁠.

• The intervals in Step (1) are, respectively, mapped to and ⁠, and the mapping formula is as follows:

  

  (18)

  where r and are the risk values before and after mapping; and are the upper and lower limits of each subinterval before adjustment; and are the upper and lower limits of the target subinterval, respectively.

The drought risk in Anhui Province from 2000 to 2020 was evaluated in this paper. According to formulas (1) − (6), the weight of each evaluation indicator could be calculated. Table 1 shows the weights calculated based on the CRITIC method.

From Table 2, it can be found that the inter-annual variation trends of the drought risk values calculated by the three methods are consistent basically, and the differences only exist in individual years. The two drought risk quantification methods based on k-means cluster points proposed in this paper not only have the ability of WCA to quantify drought risk, but also make up for the defect that it cannot classify drought risk and can effectively divide drought risk into five grades.

By comparing Figure 5(a) and 5(b) with Figure 6(a) and 6(b), it can be found that although the quantification and grade division of drought risk have been realized without introducing interval mapping, there are only minor differences in the risk values between different grades and within the same grade. However, after the introduction of interval mapping, the difference in drought risk values was obvious visually, especially the discrimination degree of risk values in different years between different grades was effectively separated. Therefore, it is effective and necessary to introduce interval mapping in this case.

Tables 3 and 4 are the comparison of the results obtained by two risk quantification methods and the drought record in statistical material. It can be found from the tables that the results obtained by two risk quantification methods are not in line with the records in the statistical material in some years.

For the one phenomenon that the assessment grade in this paper is lower than the record in the statistical material, the main reason is that Anhui Province is located in the monsoon region, and the uneven distribution of rainfall within the year leads to obvious wet and dry seasons, which easily leads to drought. However, the annual scale data selected in this paper cannot fully reflect the contradiction between the supply and demand of water and the imbalance of water resources within the year.

For the other phenomenon that the assessment grade in this paper is higher than the record in the statistical material, the main reason is that the risk grade in the yearbook represents the overall drought disaster situation in the Anhui Province which is the actual disaster after human intervention. However, the drought risk grade in this paper is comprehensively assessed from the perspectives of hazard of disaster causing factors, vulnerability of disaster bearing environment and vulnerability of disaster affected bodies, which represents the theoretical grade of drought risk that may occur. It is important to note that drought risk is not the same as drought disaster, and only when the possibility of impact and harm caused by drought becomes real, will risk translate into disaster (Qu et al. 2015). Thus, the results in this paper may be higher than the historical records.

It can be found that only 50% of the years in which the assessment results obtained by information redistribution based on IDWI matched the historical record exactly or differed by one grade. However, the result obtained by information redistribution based on MND can reach 71.43%, indicating that the use of information diffusion method to quantify drought risk can improve the rationality of the results and make it closer to the actual situation. This advantage may be caused by the following reasons: first, the regional drought system is characterized by high dimensionality, nonlinearity, correlation complexity and uncertainty (Zhang 2022). Second, the calculation principle of MND is also nonlinear, while the principle of IDWI is linear conversely (Huang et al. 2021). Third, IDWI is susceptible to the influence of points with a short distance (Ohlert et al. 2022).

In addition to the two factors mentioned in Section 3.5., the results of this paper are also influenced by the data availability. In fact, there are many indicators that can be used for drought risk assessment research. However, some data are not collected in the dataset built in this paper (some optional indicators lack systematic statistical data), so the selection of assessment indicators is limited. In addition, there is no short-term statistical data for some indicators to choose from (such as proportion of cultivated land and agricultural population), so the annual scale data selected in this paper will have a certain impact on the quantification accuracy of risk, which will result in deviations between the results in this paper and the records in statistical material.

However, it is foreseeable that with the improvement of the spatiotemporal attributes of statistical data, we can choose a shorter time scale and build a more refined risk assessment indicator system. Therefore, on the one hand, we will strengthen cooperation with the official departments to obtain more detailed statistical data while narrowing the scope of the research area. On the other hand, we will try to find the relationship between the hazard of disaster causing factors, vulnerability of disaster bearing environment, vulnerability of disaster affected bodies and the drought disaster, so as to keep the theoretical disaster situation consistent with the actual disaster situation. Thus, the above problems can be effectively solved, and the quantification of risk grades will be more accurate.

Anhui Province was taken as the research object and the annual scale assessment of drought risk was carried out in this paper. Aiming at the defects of conventional WCA and according to the classification method based on k-means cluster points, the drought risk value in the Anhui Province during 2000–2020 was quantified by IDWI and MND, and the drought risk value was refined by IMA, which can expand the way of risk assessment. The main conclusions are as follows:

• The risk of drought can be quantified by the conventional WCA, but the risk is difficult to be graded directly, which needs to be graded by other methods.

• On the basis of k-means clustering and WCA to calculate the risk value of cluster centers, IDWI and MND were used to calculate the drought risk value of each clustering member, which realized the combination of drought risk quantification and grade division.

• Although the quantification of drought risk can be realized by information redistribution based on IDWI and MND, the drought risk value obtained by MND method is more reasonable and closer to the actual situation, which benefits from its nonlinear diffusion principle.

• By introducing IMA of drought risk, the dispersion effect of risk value obtained by redistribution of information based on k-means clustering points is greatly improved. The discrimination between the risk values of the assessment object is improved, especially the risk values of different grades, so that the grades can be displayed more intuitively. Therefore, the follow-up utilization space is widened by this method, and the thinking of risk quantification in drought risk assessment is broadened.

In the future, we will try to promote the statistics of small-scale data and the establishment of relevant databases for drought risk assessment. At the same time, we will apply the method proposed in this paper to other drought-prone regions in China. For other regions, we will adjust the assessment indicators according to the data availability in the region under the premise that assessment indicators still respond to the driving mechanism of drought system.

This research was funded by the Key Science and Technology Project of Education Department of Jiangxi Province (No. GJJ201901). The authors thank Water Resources Department of Anhui Provincial and Statistics Bureau of Anhui Province, for providing the data for this study. The authors would like to thank all the reviewers who participated in the review.

W.X. did data curation, formal analysis, investigation, methodology, software, visualization, writing of the original draft. M.T. conceptualized the study, acquisition of funds, did investigation, methodology, project administration, resources, supervision, writing, review and editing of the article. Y.L. wrote the original draft.

All relevant data are available from an online repository or repositories: http://tjj.ah.gov.cn/ssah/qwfbjd/tjnj/index.html.

The authors declare there is no conflict.